A non-convex blind calibration method for randomised sensing strategies

• Published in: 2016 4th International Workshop on Compressed Sensing Theory and its Applications to Radar, Sonar and Remote Sensing (CoSeRa) pp. 16 - 20
• Main Authors: Cambareri, Valerio, Jacques, Laurent
• Format: Conference Proceeding
• Language: English
• Published: IEEE 01.09.2016
• Subjects: bilinear inverse problems; Blind calibration; Calibration; Complexity theory; Compressed sensing; computational sensing; Convergence; Inverse problems; non-convex optimisation; Radio frequency; sample complexity; Sensors
• DOI: 10.1109/CoSeRa.2016.7745690

The implementation of computational sensing strategies often faces calibration problems typically solved by means of multiple, accurately chosen training signals, an approach that can be resource-consuming and cumbersome. Conversely, blind calibration does not require any training, but corresponds to a bilinear inverse problem whose algorithmic solution is an open issue. We here address blind calibration as a non-convex problem for linear random sensing models, in which we aim to recover an unknown signal from its projections on sub-Gaussian random vectors each subject to an unknown multiplicative factor (gain). To solve this optimisation problem we resort to projected gradient descent starting from a suitable initialisation. An analysis of this algorithm allows us to show that it converges to the global optimum provided a sample complexity requirement is met, i.e., relating convergence to the amount of information collected during the sensing process. Finally, we present some numerical experiments in which our algorithm allows for a simple solution to blind calibration of sensor gains in computational sensing applications.